In this section, learning data were split into first half and second half and fit separately. The two set-sizes were fit together. Are learning outcomes for the 2 halves correlated?
#> Analysis of Variance Table
#>
#> Response: mean.acc
#> Df Sum Sq Mean Sq F value Pr(>F)
#> half 1 0.0150 0.01504 0.9589 0.3278
#> condition 3 2.7371 0.91238 58.1842 <2e-16 ***
#> half:condition 3 0.0589 0.01962 1.2511 0.2903
#> Residuals 656 10.2866 0.01568
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| condition | r | p.val |
|---|---|---|
| set3_learn | 0.341 | 0.002 |
| set3_test | 0.576 | 0.000 |
| set6_learn | 0.667 | 0.000 |
| set6_test | 0.655 | 0.000 |
#> # A tibble: 2 × 3
#> half s3 s6
#> <chr> <dbl> <dbl>
#> 1 half1 0.180 0.0986
#> 2 half2 0.147 0.0596
| condition | n | r | p.val |
|---|---|---|---|
| set3_learn | 83 | 0.130 | 0.241 |
| set6_learn | 83 | 0.258 | 0.018 |
We find that 55.4% of participants have halves 1 and 2 that fit the same model as in experiment 1. For 61.4% of participants, the first half fit the same model as in Ex1, and, 66.3% for the second half.
#> function (x, ..., wt = NULL, sort = FALSE, name = NULL)
#> {
#> UseMethod("count")
#> }
#> <bytecode: 0x7fddb44638f8>
#> <environment: namespace:dplyr>
Comparing the first half with the second half, 73.49% of participants fit the same models in the second half. This means that….[think].
These scatter plots show the differences in the distributions for
learning outcomes for subjects who fit the same models for H1 and H2 and
different
#> # A tibble: 4 × 3
#> condition t_val p_val
#> <chr> <dbl> <dbl>
#> 1 set3_learn 0.991 0.329
#> 2 set3_test -1.28 0.206
#> 3 set6_learn 0.729 0.470
#> 4 set6_test -1.01 0.320
#> # A tibble: 4 × 3
#> condition t_val p_val
#> <chr> <dbl> <dbl>
#> 1 set3_learn 1.04 0.303
#> 2 set3_test -0.114 0.909
#> 3 set6_learn -0.0821 0.935
#> 4 set6_test -1.24 0.219
#> Analysis of Variance Table
#>
#> Response: mean.acc
#> Df Sum Sq Mean Sq F value Pr(>F)
#> condition 3 2.7371 0.91238 57.9458 <2e-16 ***
#> comp 1 0.0001 0.00007 0.0046 0.9459
#> half 1 0.0150 0.01504 0.9549 0.3288
#> condition:comp 3 0.0423 0.01409 0.8948 0.4435
#> condition:half 3 0.0589 0.01962 1.2460 0.2921
#> comp:half 1 0.0046 0.00463 0.2938 0.5880
#> condition:comp:half 3 0.0367 0.01222 0.7763 0.5075
#> Residuals 648 10.2030 0.01575
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
As described above, learning data for all participants were split into the first 6 stimulus iterations and the last 6 before model fitting. Additionally, the two conditions, set-size 3 and set-size 6 were also fit separately.
#> # A tibble: 10 × 8
#> subjects name mod.id model index condition parameter param_vals
#> <int> <chr> <chr> <chr> <int> <chr> <chr> <dbl>
#> 1 6209 half1_N3 LTM_105 LTM 105 set3_learn alpha NaN
#> 2 6209 half1_N3 LTM_105 LTM 105 set3_learn egs NaN
#> 3 6209 half1_N3 LTM_105 LTM 105 set3_learn bll 1.41
#> 4 6209 half1_N3 LTM_105 LTM 105 set3_learn imag -1.41
#> 5 6209 half1_N3 LTM_105 LTM 105 set3_learn ans 1.41
#> 6 6209 half1_N6 LTM_79 LTM 79 set6_learn alpha NaN
#> 7 6209 half1_N6 LTM_79 LTM 79 set6_learn egs NaN
#> 8 6209 half1_N6 LTM_79 LTM 79 set6_learn bll 0.704
#> 9 6209 half1_N6 LTM_79 LTM 79 set6_learn imag -1.41
#> 10 6209 half1_N6 LTM_79 LTM 79 set6_learn ans 0.704
Figure x
We found that the LTM model still fit more subjects in both halves (first half- LTM: M = 52.5, RL: M = 6.5, META: M = 11.5, STR: ; second half- LTM: M = 46, RL: M = 12.5, META: M = 13, STR: ), and conditions (set-size 3 - LTM: M = 48.5, RL: M = 12, META: M = 11.5, STR: M = 11; set-size 6 - LTM: M = 50, RL: M = 7, META: M = 13, STR: M = 13) much like the results obtained through the model fitting procedure in experiment 1 (Figure 1). Furthermore, more subjects fit the LTM model in the set-size 3 condition compared to the set-size 6 condition (more in the first half than in the second half, for both), which means, for those subjects that fit the RL model, higher numbers of subjects fit RL model for set-size 6 conditions than set-size 3 (more in the second half than in the first half for both conditions). This trend aligns more with Collins (2018) findings but these results do not take into account individual dynamics (covered in detail below).
#> # A tibble: 4 × 4
#> # Groups: set_size [2]
#> set_size condition t_stat p.val
#> <chr> <chr> <dbl> <dbl>
#> 1 set3 learn 0.649 0.520
#> 2 set3 test -0.238 0.813
#> 3 set6 learn 0.326 0.746
#> 4 set6 test -0.968 0.339